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On the effective interfacial resistance through quasi-filling fractal layers

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  • Capitanelli, Raffaela
  • Pocci, Cristina

Abstract

This paper concerns the periodic homogenization of the stationary heat equation in a domain with two connected components, separated by an oscillating interface defined on prefractal Koch type curves. The problem depends both on the parameter ε that defines the periodic structure of the interface and on n, which is the index of the prefractal iteration. First, we study the limit as ε vanishes, showing that the homogenized problem is strictly dependent on the amplitude of the oscillations and the parameter appearing in the transmission condition. Finally, we perform the asymptotic behaviour as n goes to infinity, giving rise to a limit problem defined on a domain with fractal interface.

Suggested Citation

  • Capitanelli, Raffaela & Pocci, Cristina, 2017. "On the effective interfacial resistance through quasi-filling fractal layers," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 43-50.
    • Handle: RePEc:eee:chsofr:v:105:y:2017:i:c:p:43-50
    DOI: 10.1016/j.chaos.2017.09.036
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